Non-Local Robust Quaternion Matrix Completion for Large-Scale Color Image and Video Inpainting

Jia, Zhigang; Jin, Qiyu; Ng, Michael K.; Zhao, Xi-Le

doi:10.1109/tip.2022.3176133

Cited by 59 publications

(17 citation statements)

References 26 publications

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“…Based on this, we present a real structure-preserving algorithm to compute x MELS . It is proved to be a very effective method of computing quaternion matrices, and specific results are shown in [11,12,13,30,31,32,33,34,35,36].…”

Section: Data Availability Statementsmentioning

confidence: 99%

“…The least squares problem appears in many fields, such as computational mathematics, linear regression, machine learning, cybernetics and image processing. In addition, quaternions and quaternion matrices play an increasingly important role in quantum mechanics [1,2], special relativity [3,4,5], signal processing [6,7,8], relativistic dynamics [9,10], computer graphics [11,12,13] and other application fields.…”

Section: Introductionmentioning

confidence: 99%

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The solutions of the quaternion multiple equality constrained least squares problem

Zhang

Liu

2023

Preprint

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Many data models of practical problems are related to the quaternion multiple equality constrained least squares (QMELS) problem, which is a generalization of the quaternion equality constrained least squares (QELS) problem. In this paper, by utilizing the MP inverse, the quaternion QR factorization, the quaternion CS factorization and some known results of the QELS problem, we first transform the QMELS problem into an unconstrained least squares (LS) problem. Next, we give a representation formula for solutions of the QMELS problem. After that, we present a real structure-preserving algorithm of its minimum norm solution. Finally, a example is proposed to indicate the validity.

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Section: Data Availability Statementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The solutions of the quaternion multiple equality constrained least squares problem

Zhang

Liu

2023

Preprint

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show abstract

“…As an emerging mathematical tool, low-rank quaternion matrix approximation (LRQA) has attracted much attention in the field of color image processing, such as color face recognition [13,14], color image inpainting [15][16][17], and color image denoising [18,19]. A variety of LRQA-based variants are achieved by using different rank approximation regularizers [20][21][22]. Notably, Chen et al [23] proposed the quaternion nuclear norm (QNN)-based LRQA for color image denoising and inpainting.…”

Section: Introductionmentioning

confidence: 99%

Efficient quaternion CUR method for low-rank approximation to quaternion matrix

Wu,

Kou,

Cai

et al. 2024

Preprint

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The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix approximation is sometimes considerable due to the computation of the quaternion singular value decomposition (QSVD), which limits their application to real large-scale data. To address this deficiency, an efficient quaternion matrix CUR (QMCUR) method for low-rank approximation is suggested , which provides significant acceleration in color image processing. We first explore the QMCUR approximation method, which uses actual columns and rows of the given quaternion matrix, instead of the costly QSVD. Additionally, two different sampling strategies are used to sample the above-selected columns and rows. Then, the perturbation analysis is performed on the QMCUR approximation of noisy versions of low-rank quater-nion matrices. Extensive experiments on both synthetic and real data further reveal the superiority of the proposed algorithm compared with other algorithms for getting low-rank approximation, in terms of both efficiency and accuracy.

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“…n-dimensional data without modifications to architectural layers. For that reason, the already ample field of hypercomplex models based on complex [1], quaternion [2], dual quaternion [3,4], and octonion [1] numbers has been permeated by PHNNs. These networks have been defined with different known backbones such as ResNets [5,6], GANs [7,8], graph neural networks [9], and Transformers [10], among others [11,12].…”

Section: Introductionmentioning

confidence: 99%

Phydi: Initializing Parameterized Hypercomplex Neural Networks As Identity Functions

Mancanelli,

Grassucci,

Uncini

et al. 2023

2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)

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Neural models based on hypercomplex algebra systems are growing and prolificating for a plethora of applications, ranging from computer vision to natural language processing. Hand in hand with their adoption, parameterized hypercomplex neural networks (PHNNs) are growing in size and no techniques have been adopted so far to control their convergence at a large scale. In this paper, we study PHNNs convergence and propose parameterized hypercomplex identity initialization (PHYDI), a method to improve their convergence at different scales, leading to more robust performance when the number of layers scales up, while also reaching the same performance with fewer iterations. We show the effectiveness of this approach in different benchmarks and with common PHNNs with ResNets-and Transformer-based architecture. The code is available at https://github.com/ispamm/PHYDI.

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Non-Local Robust Quaternion Matrix Completion for Large-Scale Color Image and Video Inpainting

Cited by 59 publications

References 26 publications

The solutions of the quaternion multiple equality constrained least squares problem

The solutions of the quaternion multiple equality constrained least squares problem

Efficient quaternion CUR method for low-rank approximation to quaternion matrix

Phydi: Initializing Parameterized Hypercomplex Neural Networks As Identity Functions

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